A tortoise runs along a straight track, starting at position x= 0 at time t = 0. The tortoise has a velocity of v(t) =ln (1+t 2 ) inches per minute, where t is measured in minutes. a) Find the average...

A tortoise runs along a straight track, starting at position x= 0 at time t = 0. The tortoise has a velocity of v(t) =ln (1+t²) inches per minute, where t is measured in minutes.

a) Find the average acceleration of the tortoise over the time interval 0 t10 minutes. Find the instantaneous acceleration of the tortoise at time t = 10 minutes. Indicate the correct units.

b)How far does the tortoise travel between time t=0 and time t= 10 minutes?

c)At what time t,  0 to 10 , is the tortoise's instantaneous velocity equal to its average velocity over the time interval  0 to 10 ?

d) A hare begins running from the same starting position at time t = 9.5 minutes with an initial velocity b inches per minute and a constant acceleration of 2 inches per minute per minute; the hare catches up with the tortoise at time t = 10minutes. Find b.